An Operational Amplifier is basically a three-terminal device which consists of two high impedance inputs, one called the Inverting Input, marked with a negative or “minus” sign, ( - ) and the other one called the Non-inverting Input, marked with a positive or “plus” sign ( + ).
The third terminal represents the Operational Amplifiers output port which can both sink and source either a voltage or a current. In a linear operational amplifier, the output signal is the amplification factor, known as the amplifiers gain ( A ) multiplied by the value of the input signal and depending on the nature of these input and output signals, there can be four different classifications of operational amplifier gain.
- Voltage – Voltage “in” and Voltage “out”
- Current – Current “in” and Current “out”
- Transconductance – Voltage “in” and Current “out”
- Transresistance – Current “in” and Voltage “out”
The output voltage signal from an Operational Amplifier is the difference between the signals being applied to its two individual inputs. In other words, an op-amps output signal is the difference between the two input signals as the input stage of an Operational Amplifier is in fact a differential amplifier as shown below.
Differential Amplifier
The circuit below shows a generalized form of a differential amplifier with two inputs marked V1 and V2. The two identical transistors TR1 and TR2 are both biased at the same operating point with their emitters connected together and returned to the common rail, -Vee by way of resistor Re.
Differential AmplifierSo as the forward bias of transistor, TR1 is increased, the forward bias of transistor TR2 is reduced and vice versa. Then if the two transistors are perfectly matched, the current flowing through the common emitter resistor, Re will remain constant.
Like the input signal, the output signal is also balanced and since the collector voltages either swing in opposite directions (anti-phase) or in the same direction (in-phase) the output voltage signal, taken from between the two collectors is, assuming a perfectly balanced circuit the zero difference between the two collector voltages.
This is known as the Common Mode of Operation with the common mode gain of the amplifier being the output gain when the input is zero.
Operational Amplifiers also have one output (although there are ones with an additional differential output) of low impedance that is referenced to a common ground terminal and it should ignore any common mode signals that is, if an identical signal is applied to both the inverting and non-inverting inputs there should no change to the output.
However, in real amplifiers there is always some variation and the ratio of the change to the output voltage with regards to the change in the common mode input voltage is called the Common Mode Rejection Ratio or CMRR.
Operational Amplifiers on their own have a very high open loop DC gain and by applying some form of Negative Feedback we can produce an operational amplifier circuit that has a very precise gain characteristic that is dependant only on the feedback used. Note that the term “open loop” means that there are no feedback components used around the amplifier so the feedback path or loop is open.
An operational amplifier only responds to the difference between the voltages on its two input terminals, known commonly as the “Differential Input Voltage” and not to their common potential. Then if the same voltage potential is applied to both terminals the resultant output will be zero. An Operational Amplifiers gain is commonly known as the Open Loop Differential Gain, and is given the symbol (Ao).
Equivalent Circuit of an Ideal Operational Amplifier
Op-amp Parameter and Idealised Characteristic
-
Open Loop Gain, (Avo)
-
Infinite – The main function of an operational amplifier is to
amplify the input signal and the more open loop gain it has the better.
Open-loop gain is the gain of the op-amp without positive or negative
feedback and for such an amplifier the gain will be infinite but typical
real values range from about 20,000 to 200,000.
-
Infinite – The main function of an operational amplifier is to
amplify the input signal and the more open loop gain it has the better.
Open-loop gain is the gain of the op-amp without positive or negative
feedback and for such an amplifier the gain will be infinite but typical
real values range from about 20,000 to 200,000.
-
Input impedance, (Zin)
-
Infinite – Input impedance is the ratio of input voltage to
input current and is assumed to be infinite to prevent any current
flowing from the source supply into the amplifiers input circuitry ( Iin = 0 ). Real op-amps have input leakage currents from a few pico-amps to a few milli-amps.
-
Infinite – Input impedance is the ratio of input voltage to
input current and is assumed to be infinite to prevent any current
flowing from the source supply into the amplifiers input circuitry ( Iin = 0 ). Real op-amps have input leakage currents from a few pico-amps to a few milli-amps.
-
Output impedance, (Zout)
-
Zero – The output impedance of the ideal operational amplifier
is assumed to be zero acting as a perfect internal voltage source with
no internal resistance so that it can supply as much current as
necessary to the load. This internal resistance is effectively in series
with the load thereby reducing the output voltage available to the
load. Real op-amps have output impedances in the 100-20kΩ range.
-
Zero – The output impedance of the ideal operational amplifier
is assumed to be zero acting as a perfect internal voltage source with
no internal resistance so that it can supply as much current as
necessary to the load. This internal resistance is effectively in series
with the load thereby reducing the output voltage available to the
load. Real op-amps have output impedances in the 100-20kΩ range.
-
Bandwidth, (BW)
-
Infinite – An ideal operational amplifier has an infinite
frequency response and can amplify any frequency signal from DC to the
highest AC frequencies so it is therefore assumed to have an infinite
bandwidth. With real op-amps, the bandwidth is limited by the
Gain-Bandwidth product (GB), which is equal to the frequency where the
amplifiers gain becomes unity.
-
Infinite – An ideal operational amplifier has an infinite
frequency response and can amplify any frequency signal from DC to the
highest AC frequencies so it is therefore assumed to have an infinite
bandwidth. With real op-amps, the bandwidth is limited by the
Gain-Bandwidth product (GB), which is equal to the frequency where the
amplifiers gain becomes unity.
-
Offset Voltage, (Vio)
-
Zero – The amplifiers output will be zero when the voltage
difference between the inverting and the non-inverting inputs is zero,
the same or when both inputs are grounded. Real op-amps have some amount
of output offset voltage.
-
Zero – The amplifiers output will be zero when the voltage
difference between the inverting and the non-inverting inputs is zero,
the same or when both inputs are grounded. Real op-amps have some amount
of output offset voltage.
However, real Operational Amplifiers such as the commonly available uA741, for example do not have infinite gain or bandwidth but have a typical “Open Loop Gain” which is defined as the amplifiers output amplification without any external feedback signals connected to it and for a typical operational amplifier is about 100dB at DC (zero Hz). This output gain decreases linearly with frequency down to “Unity Gain” or 1, at about 1MHz and this is shown in the following open loop gain response curve.
Open-loop Frequency Response Curve
GBP = Gain x Bandwidth or A x BW.
GBP = A x BW = 10 x 100,000Hz = 1,000,000.
GBP = A x BW = 1,000 x 1,000Hz = 1,000,000. The same!.
and in Decibels or (dB) is given as:
An Operational Amplifiers Bandwidth
The operational amplifiers bandwidth is the frequency range over which the voltage gain of the amplifier is above 70.7% or -3dB (where 0dB is the maximum) of its maximum output value as shown below.
Operational Amplifier Example No1.
Using the formula 20 log (A), we can calculate the bandwidth of the amplifier as:
37 = 20 log A therefore, A = anti-log (37 ÷ 20) = 70.8
GBP ÷ A = Bandwidth, therefore, 1,000,000 ÷ 70.8 = 14,124Hz, or 14kHz
Then the bandwidth of the amplifier at a gain of 40dB is given as 14kHz as previously predicted from the graph.Operational Amplifier Example No2.
If the gain of the operational amplifier was reduced by half to say 20dB in the above frequency response curve, the -3dB point would now be at 17dB. This would then give the operational amplifier an overall gain of 7.08, therefore A = 7.08.If we use the same formula as above, this new gain would give us a bandwidth of approximately 141.2kHz, ten times more than the frequency given at the 40dB point. It can therefore be seen that by reducing the overall “open loop gain” of an operational amplifier its bandwidth is increased and visa versa.
In other words, an operational amplifiers bandwidth is inversely proportional to its gain, ( A 1/∝ BW ). Also, this -3dB corner frequency point is generally known as the “half power point”, as the output power of the amplifier is at half its maximum value as shown:
Operational Amplifiers Summary
We know now that an Operational amplifiers is a very high gain DC differential amplifier that uses one or more external feedback networks to control its response and characteristics. We can connect external resistors or capacitors to the op-amp in a number of different ways to form basic “building Block” circuits such as, Inverting, Non-Inverting, Voltage Follower, Summing, Differential, Integrator and Differentiator type amplifiers.
Op-amp SymbolThere are a very large number of operational amplifier IC’s available to suit every possible application from standard bipolar, precision, high-speed, low-noise, high-voltage, etc, in either standard configuration or with internal Junction FET transistors.
Operational amplifiers are available in IC packages of either single, dual or quad op-amps within one single device. The most commonly available and used of all operational amplifiers in basic electronic kits and projects is the industry standard μA-741.
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